Extended Kalman filtering based parameter estimation and drift compensation for a MEMS rate integrating gyroscope

Abstract This paper presents an offline extended Kalman filtering based parameter identification and drift compensation for a MEMS ring vibratory gyroscope. Damping and stiffness imperfections are the major error sources in MEMS vibratory gyroscopes. In the rate integrating operation mode, where angle is output instead of angular velocity as in the case of the rate gyroscope, parameter identification is an essential prerequisite for any feedback control and compensation algorithm to minimize angle drift and other errors. The proposed EKF method provides five estimates for the resonator DC loop gain, and another four parameters related to the non-proportional damping and aniso-elasticities. The method is based on the slowly varying averaged dynamic model expressed in terms of orbital elements. The averaging methodology offers important advantages over similar attempts based directly on the dynamic model expressed in terms of fast time varying displacement and velocity of vibration. Firstly, the observed measurements are subjected to significantly lower levels of noise as a consequence of the narrowband demodulation process employed in the calculation of the orbital elements. Secondly, the EKF requires much lower update rate due to the slowly varying nature of the augmented states. These advantages result in a more accurate estimation, improved stability performance and the possibility for real time implementation of the EKF. Numerical simulation and offline implementation of the EKF using experimental gyroscope operation data are provided to validate the proposed method. Moreover, the identified damping imperfections have been used in the drift compensation control in a DSP based real time rate integrating gyroscope control system. Ultimately, the maximum angular drift has been reduced to 1° per second. Spectrum analysis shows the angle drift error is dominated by 4th harmonics caused by dynamics not included in the conventional gyroscope model.

[1]  Hyochoong Bang,et al.  Imperfection Parameter Observer and Drift Compensation Controller Design of Hemispherical Resonator Gyros , 2013 .

[2]  Roberto Horowitz,et al.  Dynamics and control of micromachined gyroscopes , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[3]  Zhongxu Hu,et al.  Control and damping imperfection compensation for a rate integrating MEMS gyroscope , 2015, 2015 DGON Inertial Sensors and Systems Symposium (ISS).

[4]  Igor P. Prikhodko,et al.  Overcoming limitations of Rate Integrating Gyroscopes by virtual rotation , 2016, 2016 IEEE International Symposium on Inertial Sensors and Systems.

[5]  Miroslav Šimandl,et al.  Parameter Estimation of MEMS Gyroscope Using Local State Estimation Methods , 2015 .

[6]  K. Najafi,et al.  Novel mismatch compensation methods for rate-integrating gyroscopes , 2012, Proceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium.

[7]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[8]  Steve Gibson,et al.  System Identification of a MEMS Gyroscope , 2001 .

[9]  Roberto Horowitz,et al.  Dynamics and control of a MEMS angle measuring gyroscope , 2008 .

[10]  Andrei M. Shkel,et al.  Identification of anisoelasticity for electrostatic trimming of rate-integrating gyroscopes , 2002, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[11]  Parsa Taheri-Tehrani,et al.  A new electronic feedback compensation method for rate integrating gyroscopes , 2016, 2016 IEEE International Symposium on Inertial Sensors and Systems.

[12]  Bernard Friedland,et al.  A nonlinear observer for estimating parameters in dynamic systems , 1997, Autom..

[13]  Barry Gallacher,et al.  Principles of a Micro-Rate Integrating Ring Gyroscope , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[14]  B. Friedland,et al.  Theory and error analysis of vibrating-member gyroscope , 1978 .

[15]  Claus-Peter Fritzen,et al.  Identification of mass, damping, and stiffness matrices of mechanical systems , 1986 .

[16]  Tsung-Lin Chen,et al.  Compensation of interface circuit errors for MEMS gyroscopes using state observers , 2008, 2008 3rd International Conference on Sensing Technology.

[17]  Sungsu Park.  Adaptive Control of a Vibratory Angle Measuring Gyroscope , 2010, Sensors.

[18]  Henk Nijmeijer,et al.  Modelling the dynamics of a MEMS resonator : simulations and experiments , 2008 .

[19]  Zhongxu Hu,et al.  A systematic approach for precision electrostatic mode tuning of a MEMS gyroscope , 2014 .

[20]  Ashwin A. Seshia,et al.  Identification of Anisoelasticity and Nonproportional Damping in MEMS Gyroscopes , 2004 .